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Half of Ethan's string is equal to 2/3 of Kayla's string. The total length of their strings is 10 feet. How much longer is Ethan's string than Kayla's? Drawing

User Pindiwala
by
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2 Answers

2 votes

Answer:

Ethan's string is
=(10)/(7) feet longer than Kayla's string.

Explanation:

Let Ethan's string = x feet

and Kayla's string = y feet

According to question,

Half of Ethan's string is equal to 2/3 of Kayla's string that is,


(1)/(2)x=(2)/(3)y


\Rightarrow x=(4)/(3)y ..............(1)

Also,The total length of their strings is 10 feet that is,


x+y=10

Put value of x from (1),


(4)/(3)y+y=10

Solving for y, we get,


\Rightarrow y((4)/(3)+1)=10


\Rightarrow y((4+3)/(3))=10


\Rightarrow y((7)/(3))=10


\Rightarrow y=(10 * 3)/(7)


\Rightarrow y=(30)/(7)

Thus, Length of Kayla's string is
(30)/(7) feet.

and Put value of y in (1) to get value of x,


\Rightarrow x=(4)/(3) * (30)/(7)


\Rightarrow x=(40)/(7)

Thus, Length of Ethan's string is
(40)/(7) feet.

Length of Ethan's string is longer than Kayla's string = Length of Ethan's string-Length of Kayla's string.


=(40)/(7)-(30)/(7)


=(10)/(7)

Thus, Ethan's string is
=(10)/(7) feet longer than Kayla's string.


Half of Ethan's string is equal to 2/3 of Kayla's string. The total length of their-example-1
1 vote

Answer:
(10)/(7) meters


Explanation:

Let x be the length of Kaya's string and y be the length of Ethan's string

Then According to the question, we have the following equations


(1)/(2)y=(2)/(3)x\\\Rightarrow\ y=(4)/(3)x......(1)\\x+y=10....(2)

Substitute the value of y from (1) in (2), we get


(4)/(3)x+x=10\\\Rightarrow(4x+3x)/(3)=10\\\Rightarrow\ (7x)/(3)=10\\\Rightarrow\ x=(30)/(7)

The length of Kaya's string =
(30)/(7) feet

The length of Ethan's string =
(4)/(3)*(30)/(7)=(40)/(7) meters

The difference in their lengths=
(40)/(7)-(30)/(7)=(10)/(7)

Hence, Ethan's string is
(10)/(7) meters longer than the Kaya's string.



User Stefanos Kalantzis
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